Wind Velocity Effect on the Aerodynamic and Acoustic Behavior of a
Vertical Axis Wind Turbine
MEROUANE HABIB
Department of Mechanical Engineering,
University of Mascara,
ALGERIA
Abstract: - In this work we present a numerical study on the effect of wind velocity on the aerodynamic and
acoustic behavior of a Savonius-type vertical axis wind turbine (VAWT). The study focuses on the prediction of
the torque coefficient for different flow velocities and rotational velocities of the wind turbine. We also present the
triggering of the wake zone near the wind turbine blades to see the dynamic effect on the behavior of the wind
turbine. The study of the numerical simulation is carried out using a fluent CFD calculation code using the finite
volume method for the discretization of the differential equations. The equations governing the flow are solved by
the SIMPLE algorithm using two K-epsilon turbulence models.
Key-Words: - Wind turbine; Savonius turbine; Aerodynamics wind turbine; wind turbine sound, vertical axis
turbine; Aero-acoustic.
Received: March 15, 2023. Revised: February 7, 2024. Accepted: March 6, 2024. Published: April 25, 2024.
1 Introduction
The Savonius vertical wind turbine consists of two or
more blades attached directly to the vertical axis in
opposite directions. The wind turbine is driven by the
force of the wind which turns the rotor by producing
mechanical energy that can be transformed into
electrical energy through a generator.
With its simplicity, the Savonius vertical wind
turbine fits into the roofs of buildings without
altering their aesthetics. It can also be installed at the
top of a mast. Discreet and silent, it works even in
light winds, but remains unsuitable for producing
large amounts of electricity. The Savonius wind
turbine has many variations, including a very
fashionable helical version that optimizes wind
resistance.
The Savonius wind turbine works on the
principle of differential drag: the convex part has a
drag force (force opposing the movement of the
wind) less than the drag force of the concave part.
This difference between the forces creates a torque
that turns the wind turbine.
The Savonius wind turbines type are generally
used in domestic buildings to produce electrical
energy and can also be used in a hybrid system with
artificial intelligence (solar panel-Savonius wind
turbine) to operate small power machines such as
pumping water in agricultural areas
Many researchers have extensively studied the
performance of vertical-axis wind turbines through
experimental and numerical studies, [1], [2], [3], [4],
[5], [6], [7] [8], [9].
The authors [10], studied by experiment in a
Wind Tunnel the performance of a Savonius Rotor in
the flow field. His study describes the experimental
evaluation of the unsteady flow field downstream the
rotor using a constant temperature hot wire
Anemometer (CTA). Whilst, for performance
analysis. The torque measurements have been
obtained directly from the Servo Amplifier torque
monitor. They indicate that the torque coefficient
depends linearly with the tip velocity ratio, with the
highest value at the lowest λ
The authors [11], have investigated
experimentally and numerically the flow around a
vertical axis Savonius- type wind turbine. The rotor
has two blades and a height that is approximately
equal to the diameter of the rotor. His results confirm
the ability of the modeling of detached vortex
simulations to represent the turbulent detached flow
well. Thus, this type of turbulence modeling can be
applied to analyze and optimize the Savonius wind
turbine as well as another drag-type wind turbine.
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The results obtained for the power coefficient show
that they are very close to the experimental data.
The performance of the axial wind turbine is
studied by experiment with different types of blades
two-bladed in a wind tunnel, [12]. The two-bladed
turbine is tested in an open type test section and its
performance is assessed in terms of power and torque
coefficients. The experiments have also been
conducted with other standard blades such as semi-
circular, semi-elliptic, Benesh and Bach types to have
a direct comparison. His investigation demonstrates
that a gain of 34.8% in maximum power coefficient
with the newly developed two-bladed turbine.
The authors [13], carried out a noise
investigation of small-scale vertical axis wind
turbines in urban areas and they observed that the
process of upstroke in the windward rotor regions
(20◦∼130◦) and downstroke in the leeward rotor
regions (200◦ ∼ 310◦) are the main mechanisms
generating noise due to the dynamic stall effect. The
windward side of VAWTs constitutes a significant
noise source region. With an increase in wind
velocity, the effect of self-induced turbulence on the
noise characteristics varies depending on the
operating state of the VAWTs. According to their
results, under a wind velocity of 10 m/s at night, the
noise emitted by VAWTs reaches the noise control
standard of some countries at distances of more than
260 m
The authors [14], presented low noise prediction
for a VAWT operating at a low 𝑅𝑒 number. They
used the low fidelity method which is based on the
actuator cylinder model coupled with semi-empirical
models for airfoil self-noise and turbulence
interaction noise. Their results showed good
agreement between the high-fidelity simulations and
the low-fidelity model at low frequencies, where
turbulence interaction noise is the dominant noise
source. At higher frequencies, airfoil-specific noise
dominates and existing methods, based on stable
airfoils, do not predict noise correctly. His work
shows that the presented low-fidelity model predicts
turbine aerodynamics and aeroacoustics with
acceptable accuracy for a design stage. However,
improvements are needed to better predict the far-
field noise of blades in an unstable field
2 Mathematical Modelling
2.1 Standard k-ε Turbulence Model
The k-epsilon model is the most used for the
prediction of turbulent flows. This model is based on
the Boussinesq approximation. This hypothesis
corresponds to relating the Reynolds stresses to the
mean gradients of turbulent velocity and viscosity.
ij
i
j
j
i
tji k
x
u
x
u
uu
3
2
(1)
Where k is the turbulent kinetic energy, defined as:
iiuuk
2
1
(2)
Turbulent viscosity is modeled as follows:
2
k
C
t
(3)
With ε is the dissipation rate given by:
j
i
j
it u
u
u
u
(4)
For the k-epsilon model the two additional equations
are given:
jk
t
j
i
ix
k
x
uk
x
k
t
kMbk SYGG
(5)
j
t
j
i
ixx
u
xt
S
k
CGCG
k
Cbk
2
231
(6)
Where
Gk and Gb are the kinetic energy of turbulence due to
mean velocity gradients and buoyancy, respectively.
1
C
,
2
C
, and
3
C
are the constants given in Table 1.
k
and
are the turbulent Prandtl numbers for k and
respectively given in Table 1.
k
S
et
S
are the source terms for k and ε respectively.
The kinetic energy of turbulence due to mean
velocity gradients is modeled as:
i
i
jik x
u
uuG
(7)
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The kinetic energy of turbulence due to buoyancy is
given by:
it
t
ib x
T
Pr
gG
(8)
Where
is the coefficient of thermal expansion.
The coefficients of the models are given in Table 1:
Table 1. Constants of the standard k – ε model
μ
C
1ε
C
2ε
C
3ε
C
k
σ
ε
σ
0, 09
1, 44
1, 92
0.5
1, 0
1, 3
The coefficient of power of a wind turbine
SRV
p
Cp
2
2
1
(9)
With P is the maximum power obtained from the
wind
SRV
C
Cm
2
2
1
(10)
mp CC
(11)
With λ is the Tip speed ratio between tangential
velocity from the rotor tip and the free-flow velocity
of the wind
V
R
(12)
Where
ω : is the angular velocity of the rotor and R is the
radius of the rotor
2.2 Modeling of Acoustic Waves
For the prediction of sound waves around the blades
of the wind turbine, the Broadband Noise Source
Models model was used for an isotropic turbulent
flow whose acoustic power is determined by the
following relationship:
5
0
53
0a
uu
PA
(13)
where
u
is turbulence velocity
is length scales
0
a
is the velocity of sound.
is a model constant.
The sound field produced by the turbulent flow
around a solid body for very low Mach numbers is
given after Curle's integral [15] by the following
relation:
yds,y
t
p
r
nyx
a
t,xp S
iii
2
0
1
(14)
where
is the emission time
S is the integration surface
The sound intensity in the far field can be written:
ydsyA,y
t
p
r
cos
a
pc
S
2
2
2
2
0
2
2
16
1
(15)
where
Ac is the correlation area
3 Grid and Computational Domain
The Savonius wind turbine is made up of two semi-
cylindrical blades offset from each other by a distance
a and e with diameter D. The various geometric
parameters of the wind turbine are mentioned in the
Figure. 1 The height of the blades H = 1.8 m, H/D =
1.6, e = 0.16D, a / D = 0
The mesh was carried out using the gambit
software with triangular meshes and 28416 nodes; the
domain of the mesh is devised in two parts, the first
one with a fixed mesh and the second with a moving
mesh
4 Boundary Condition
The boundary conditions are defined in the extremity
of the computational domain, at the inlet condition a
velocity flow value is imposed to (4, 6 and 8 m/s), at
the outlet of the flow a atmospheric pressure is
maintained, the wind turbine is limited by two walls
(Wall conditions). The rotation velocity can be varied
for n = 70 to 90 rpm
The wind turbine simulation domain has axial and
radial distances of 16 and 10 m respectively to form a
rectangle where the wind turbine is placed in its
center
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Fig. 1: Configuration of the Savonius wind turbine
5 Results and Discussion
In this section we present the main results obtained by
numerical simulation using the k-epsilon model for
the prediction of turbulence around the blades of the
wind turbine and the Broadband Noise Source model
for the prediction of the acoustic waves
To evaluate the performance of the wind turbine
at all points of its operation, three wind velocity
values were chosen (4, 6, and 8 m/s) and three times
intervals of 0.2, 0.4 and 0.6 s. The wind velocity
values, the corresponding angular velocities and the
time steps used for each calculation are summarized
in Table 2 and Table 3.
Table 2. The first step
Table 3. The second step
Figure 2, Figure 3 and Figure 4 show the mean
velocity field for different wind velocities (4, 6, and 8
m/s) and three calculation times (0.2, 0.4, and 0.6 s).
We observe in these figures that the field of the mean
velocity is important around the blades of the wind
turbine mainly in the sides of the upper surface of the
blade which turns in the same direction as the wind.
This velocity decreases to reach zero values behind
the rotor witch created by a significant depression.
Figure 5, Figure 6 and Figure 7 show the
distribution of the pressure coefficient for different
wind velocities (4, 6, and 8 m/s) and three calculation
times (0.2, 0.4, and 0.6 s). We observe in these figures
the pressure coefficient depends only on the
orientation of the Savonius rotor. A very high-
pressure coefficient is observed upstream of the
Savonius rotor which is in opposition with the
velocity wind direction in the convex part of the
blade. At the concave surface of the blade, there is a
strong depression which gives a very low pressure
coefficient. The most important areas of depression
also appear in the central region of the Savonius rotor.
This depression zone extends downstream of the rotor
to the exit of the domain.
Figure 8 shows the torque coefficient obtained by
the numerical simulation for different flow conditions
(different wind velocities 4, 6, and 8 m/s,
respectively). The results indicate that the torque
coefficient has a positive and a negative sign with
maximum and minimum values for all different flow
conditions, the torque coefficient is important when
the wind velocity is higher than 8 m/s. At wind
velocity equal to 8 m/s the torque coefficient is
positive for the intervals angle situated between 120°
to 240° and negative for the angles situated between
0° to 100°, 280° to 360°
Figure 9 presents the torque coefficient for
different angular velocities of the Savonius rotor 70,
80, and 90 rpm in moderate velocity wind 6 m/s. The
results indicate that the torque coefficient depends
also on the angular velocity of the Savonius rotor. We
observe a phase shift between the curves which can be
explained by the variation in the frequency of the
angular velocity
Figure 11, Figure 12 and Figure 13 show the
sound power level contours for different time
intervals. It is observed in these figures that the
acoustic power is mainly concentrated at the level of
the blades of the Savonius turbine and mainly in the
upper part of the blades, this acoustic power is very
low of the order of 30 dB for a very low wind velocity
in occurrence for 4 m/s, the sound field increases
according to the increase in wind velocity and
according to the orientation of the blades of the wind
turbine. We note that this acoustic power strongly
depends on the angle of orientation of the blades
Table 4 and Table 5 present the statistical results
of the maximum and minimum torque coefficient
during the stabilized operation of the Savonius wind
turbine for the case where the wind velocity is
Wind
velocity
Angular
velocity
Times
4
80 rpm
0.2 s, 0.4 s , 0.6 s
6
8
Wind
velocity
Angular
velocity
Times
6 m/s
70 rpm
0.2 s, 0.4 s , 0.6 s
80 rpm
90 rpm
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variable from 4, 6, and 8 m/s and an angular velocity
of the rotor is maintained constant 80 rpm, for the
second case the wind velocity is kept constant and the
angular velocity of the rotor is variable from 70, 80
and 90 rpm. We notice that the values of the
maximum torque coefficients have positive signs
which are important for the case where the wind
velocity is 8 m/s with a value of +0.46 and for the
case where the wind velocity is 6 m/s and an angular
velocity of 90 rpm with a value of +0.46. We also
notice that there are minimum values of the negative
torque coefficients for the case where the wind
velocity is 8 m/s with a value of - 0.15 and - 0 .13 for
the case when the wind velocity is 6 m/s and an
angular velocity of 70 rpm.
Table 4. Statistical results for the first step
Table 5. Statistical results for the second step
Fig. 2: The average velocity field at different calculation times for wind velocity 4 m/s
Fig. 3: The average velocity field at different calculation times for wind velocity 6 m/s
Fig. 4: The average velocity field at different calculation times for wind velocity 8 m/s
Wind
velocity
Angular
velocity
Maximum
torque
coefficient
Minimum
torque
coefficient
4
80 rpm
+ 0.25
+ 0.1
6
+ 0.38
+ 0.04
8
+ 0.46
- 0.15
Wind
velocity
Angular
velocity
Maximum
torque
coefficient
Minimum
torque
coefficient
6 m/s
70 rpm
+ 0.28
- 0 .13
80 rpm
+ 0.38
- 0.05
90 rpm
+ 0.46
- 0.09
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Fig. 5: The pressure coefficient at different calculation times for wind velocity 4 m/s
Fig. 6: The pressure coefficient at different calculation times for wind velocity 6 m/s
Fig. 7: The pressure coefficient at different calculation times for wind velocity 8 m/s
Fig. 8: Torque coefficient for different flow wind velocity (4, 6 and 8 m/s)
0100 200 300 400 500 600 700 800
-0,4
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
n=80 rpm
Torque coefficient
Relative angle (°)
Wind velocity V=4 m/s
Wind velocity V=6 m/s
Wind velocity V=8 m/s
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0
30
60
90
120
150
180
210
240
270
300
330
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
Torque coefficient
n=80 rpm
Wind velocity V=4 m/s
Wind velocity V=6 m/s
Wind velocity V=8 m/s
Time =0.6 s
Time = 0.2 s
Time =0.4 s
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Fig. 9: Torque coefficient for different rotor velocity (70, 80 and 90 rpm)
Fig. 10: Power and Torque coefficients for various Tip speed ratio (TSR)
Figure 10 shows the Power and Torque
coefficients for various Tip velocity ratios (TSR). We
observe in this figure that the optimal point of the
torque coefficient is obtained at 0.43 TSR with a
value of 0.46. The wind turbine can generate a
maximum power coefficient at Cp=0.31 to 1.2 TSR
Fig. 11: The acoustic power level at different calculation times for wind velocity 4 m/s
0100 200 300 400 500 600 700 800
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Wind velocity V=6 m/s
Torque coefficient
Relative angle (°)
n=70 rpm
n=80 rpm
n=90 rpm
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0
30
60
90
120
150
180
210
240
270
300
330
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
Wind velocity V=6 m/s
n=70 rpm
n=80 rpm
n=90 rpm
0,2 0,4 0,6 0,8 1,0 1,2
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
Power and torque coefficients
TSR
Torque coefficient
Power coefficient
Time = 0.2 s
Time =0.4 s
Time =0.6 s
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Fig. 12: The acoustic power level at different calculation times for wind velocity 6 m/s
Fig. 13: The acoustic power level at different calculation times for wind velocity 8 m/s
6 Conclusion
In this study, an unsteady numerical simulation was
carried out with the CFD code to understand the
aerodynamic and acoustic behavior during the
operation of a vertical axis wind turbine of the
Savonius type. The results indicate that the torque
coefficient depends only on the wind velocity and the
rotational velocity angle of the Savonius turbine. The
Savonius wind turbine has fairly low torques with
maximum and minimum amplitudes with a positive
and negative value; these values depend essentially on
the rotational velocity angle. In this study the torque
coefficient is positive for the intervals angle situated
between 120° to 240° and negative for the angles
situated between 0° to 100°, 280° to 360°. For
acoustic power it is observed that the acoustic power
is mainly concentrated at the level of the blades of the
Savonius turbine and mainly in the upper part of the
blades, this acoustic power is very low the order of 30
dB for a very low wind velocity in occurrence for 4
m/s, the sound field increases according to the
increase in wind velocity and according to the
orientation of the blades of the wind turbine. We note
that this acoustic power strongly depends on the angle
of orientation of the blades
The next future work will be on the aero-
acoustics of vertical-axis turbines with different blade
shapes and different positions.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The author contributed in the present research, at all
stages from the formulation of the problem to the
final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The author has no conflicts of interest to declare
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